Enrolments in postgraduate engineering in Australia include a significant proportion of Asian ESL (English as a Second Language) students, and there is some debate in the literature about whether they are capable of critical appraisal. Content-based discipline-specific EAP (English for Academic Purposes) courses provide an environment for addressing the language, writing, and critical appraisal needs of such students. In particular, there is evidence that a 'sustained' approach to critical appraisal through engaging with engineering content is the best environment for this significant cohort. Despite this, such programmes are relatively rare in higher education partly as a result of the peripheral status of language and academic skills in relation to engineering knowledge and practice. This case study outlines the curriculum framework and rationale for a content-based EAP response to teaching critical appraisal skills and examines evaluative feedback from an open-ended survey of three semester cohorts of students (n=64, 85% response rate) regarding their encounter with critical thinking and practice. The paper argues both that discipline-specific EAP courses are an appropriate place to teach critical appraisal skills and contributes to the debate on the capacity of ESL students to develop this skill.